The purpose of this paper is to investigate the relationship between the associated primes of non-zero factors of a uniform injective module over a Noetherian ring and the right clique of the assassinator, when the clique satisfies the second layer condition. We introduce the terminology “representationally replete” to refer to primes where every linked prime occurs as such an associated prime and we study this property in several classes of rings including enveloping algebras of solvable Lie algebras and finite dimensional algebras